Figure 1.

Effects of attractor network dynamics on belief updating. This schematic illustrates the energy landscapes of two Hopfield-type networks each with two basins of attraction. Continuous black line indicates a normal network whose basins of attraction are relatively deep. Dotted black line indicates the effect of NMDAR (or cortical dopamine 1 receptor) (Durstewitz and Seamans, 2008; Redish et al., 2007) hypofunction (Abi-Saab et al., 1998; Javitt et al., 2012) on the energy landscape: the attractor basins become more shallow. We assume that Basins A and B correspond to different inferences about (hidden) states in the world (e.g., one jar or another being the source of beads in the beads task). Dots indicate the networks' representations of either control or Scz subjects' beliefs about these hidden states. Such networks are highly reminiscent of Hopfield networks with two stored representations; in this case, the representations correspond to inferences about hidden states, rather than memories. Arrows indicate the changes in network states resulting from sensory evidence for (solid arrows) or against (dashed arrows) the current inference. When the attractor basin is shallower, it is harder for supportive evidence to stabilize the current state much further, but it is easier for contradictory evidence, or just stochastic neuronal firing, to shift the current network state toward an alternative state. These changes in network dynamics may also be reflected in the inferences the network computes (i.e., easier switching between attractor basins may correspond to easier switching between beliefs), although this is yet to be demonstrated experimentally. NMDAR hypofunction could contribute to an increased tendency to switch between beliefs and increased stochasticity in responding in several ways (Rolls et al., 2008): (1) by reducing inhibitory interneuron activity, via weakened NMDAR synapses from pyramidal cells to interneurons, such that other attractor states are less suppressed when one is active (a spiking network model has shown that this leads to more rapid initial belief updating in perceptual tasks) (Lam et al., 2017); (2) by reducing pyramidal cell activity, via weakened recurrent NMDAR synapses on pyramidal cells, such that attractor states are harder to sustain; and (3) by reducing the NMDAR time constant, making states more vulnerable to random fluctuations in neural activity. See also similar schematics elsewhere (Durstewitz and Seamans, 2008; Rolls et al., 2008).